Form factors of two-hadron states from a covariant finite-volume formalism

Baroni, Alessandro; Briceño, Raúl A.; Hansen, Maxwell T.; Ortega-Gama, Felipe G.

doi:10.1103/physrevd.100.034511

Cited by 49 publications

(105 citation statements)

References 83 publications

(170 reference statements)

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“…As discussed in some detail in Refs. [7,8], the analytic structure of W µ is significantly more complicated than that of M. One can identify three generic sources of non-analyticity in the 2 + J → 2 amplitude: (i ) Exactly as for M, diagrams with on-shell two-particle intermediate states lead to factors of ρ(s). W µ thus exhibits the same branch cut and multi-sheet structure as M. (ii ) Isolated poles arise due to the subtracted diagrams in Fig.…”

Section: B 2 + J → 2 Amplitudes and Form Factorsmentioning

confidence: 99%

“…We consider a method, first introduced in Refs. [7,8], that allows one to determine such quantities from numerical LQCD. remove binding-momentum-enhanced finite-volume artifacts.…”

Section: Introductionmentioning

confidence: 99%

“…II, 2 + J → 2 transition amplitudes allow one to extract elastic form factors of bound states and resonances, thereby providing direct information on the structure of these states and possibly resolving which models are most descriptive [79][80][81]. As compared to the transitions described in the preceding paragraph, the necessary formalism for these quantities is significantly more complicated [7,8,20,82]. 3 Building on previous work, in Ref.[7] two of us derived a model-independent relation between the corresponding finite-volume matrix elements, schematically denoted 2|J |2 L (where L indicates the side-length of the periodic cubic volume), and the 2 + J → 2 transition amplitude, W. In Ref.[8] we improved the method by simplifying technical details relating to the onshell projection of the single-particle form factor and by using Lorentz covariant poles in the various finite-volume kinematic functions that arise.…”

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confidence: 99%

“…III.The purpose of this work is to provide two non-trivial checks on the general relations of Refs. [7,8], and also to demonstrate their predictive power even in simplified special cases. As a first check, in Sec.…”

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confidence: 99%

“…The results of this work stress that it is important to pursue the same paradigm for matrix elements of loosely bound states, using the formalism of Refs. [7,8] to non-perturbatively…”

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confidence: 99%

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Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states

2019

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Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide non-trivial checks on the final results and also to explore limiting cases in which more straightforward predications may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume-independent and equal to the total charge of the two-particle state. Second, we study the implications for a twoparticle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron's scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite-series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state. * 1 Similar outstanding puzzles are present in the heavy quark sector; see Refs.[5] and [6] for recent reviews. arXiv:1909.10357v1 [hep-lat] 23 Sep 2019The primary formal challenge arises from the fact that LQCD calculations are necessarily performed in a finite Euclidean spacetime, where the definition of asymptotic states is obscured. One of the leading methods to overcome this issue is to derive and apply non-perturbative mappings between finite-volume energies and matrix elements (directly calculable via numerical LQCD) and infinite-volume scattering and transition amplitudes. 2 This approach was first introduced by Lüscher [13,14], in seminal work relating the spectrum of two-particle states in a cubic volume with periodicty L, to the corresponding infinite-volume amplitudes. The idea has since been extended for arbitrary two-particle scattering [15][16][17][18][19][20][21][22][23] and more recently to three particles [24][25][26][27][28][29][30][31][32][33], with the latter currently limited to identical scalars (or pseudoscalars). The two-particle relations have made possible the determination of hadronic scattering amplitudes for a wide range of particle species [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], including energies where multiple channels are kinematically open [53][54][55][56][57][58][59][60][61]. Most recently, the first LQCD calculations to constrain three-particle interactions using excited states were performed in Refs. [62][63][64].Electroweak interactions involving scattering states can also be accessed using LQCD, via a generalization of the methods described above. The ...

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Section: B 2 + J → 2 Amplitudes and Form Factorsmentioning

confidence: 99%

“…We consider a method, first introduced in Refs. [7,8], that allows one to determine such quantities from numerical LQCD. remove binding-momentum-enhanced finite-volume artifacts.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…The results of this work stress that it is important to pursue the same paradigm for matrix elements of loosely bound states, using the formalism of Refs. [7,8] to non-perturbatively…”

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confidence: 99%

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Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states

2019

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Decay amplitudes to three hadrons from finite-volume matrix elements

Hansen

Romero-López

Sharpe

2021

J. High Energ. Phys.

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We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

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Dispersion relations for hadronic light-by-light scattering in triangle kinematics

Lüdtke

Procura

Stoffer

2023

J. High Energ. Phys.

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We present a new strategy for the dispersive evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon aμ. The new approach directly applies in the kinematic limit relevant for aμ: one of the photons is treated as an external electromagnetic field with vanishing momentum, so that the kinematics corresponds to a triangle. We derive expressions for the relevant single-particle intermediate states, as well as the tensor decompositions of the two-pion sub-processes that appear in addition to those needed in the established dispersive approach. The existing approach is based on a set of dispersion relations for the hadronic light-by-light tensor in four-point kinematics. At present it is not known how to consistently include in this framework resonant intermediate states of spin 2 or larger, due to the appearance of kinematic singularities that can be traced back to the redundancy of the tensor decomposition. We show that our new approach circumvents this problem and enables dispersion relations in the limit of triangle kinematics that are manifestly free from kinematic singularities, paving the way towards a data-driven evaluation of all relevant exclusive hadronic intermediate states.

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Form factors of two-hadron states from a covariant finite-volume formalism

Cited by 49 publications

References 83 publications

Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states

Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states

Decay amplitudes to three hadrons from finite-volume matrix elements

Dispersion relations for hadronic light-by-light scattering in triangle kinematics

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